209 A. A. Fraenkel’s Philosophy of Religion: A Translation of “Beliefs and Opinions in 1 Light of the Natural Sciences” By: M. ZELCER Introductory Essay 1 – Life Abraham Adolf Halevi Fraenkel is best known to mathematicians and philosophers as one of the founders of modern set theory. From the late 1800s through the 1930s, modern logic and set theory emerged as part of the new program to establish reliable and secure foundations for mathematics. Logicians and set theorists were then devising the methodology that would shape the way mathematics is currently practiced. Mathematicians and philosophers like Georg Cantor, Gottlob Frege, David Hilbert, Bertrand Russell, Alfred N. Whitehead, Richard Dedekind, Ernst Zermelo, and Kurt Gödel were making fundamental contributions to the foundations of ma- thematics. Though his early mathematical work was in the field of algebra, Fraenkel’s most notable contribution was in the theory of sets. He and Ernst Zermelo formulated a set theory that should be not susceptible to the famous paradox of Russell, or the Burali-Forti .המאמר הזה הוא זל "נ סבי, ר' ירחמיאל זעלצער ז"ל 1 Thanks to Shaul Katz for bringing Fraenkel’s article to my attention many years ago in a discussion about the history of the Hebrew Universi- ty; Heshey Zelcer for his assistance with the translation; Dahlia Koz- lowsky for stylistic comments; and Noson Yanofsky for many valuable suggestions; a few footnotes are due entirely to him. Also, thanks to Tina Weiss at the HUC library for help tracking down some of Fraenkel’s essays. ________________________________________________________ Meir Zelcer received a PhD in philosophy from the City University of New York Graduate Center. Ḥ akirah 12 © 2011 210 : Hakirah,̣ the Flatbush Journal of Jewish Law and Thought paradox.2 The set theory he helped develop is the most popular and is known as Zermelo-Fraenkel set theory, or ZFC. To understand the relevance of ZFC consider that the vast majority of modern ma- thematics can be formulated with, and be seen as being built upon, sets and ZFC’s few simple axioms is their foundation. Most work- ing mathematicians usually do not think about the axioms, nor do they care if their work can be put into the language of ZFC. Never- theless, with enough effort, their work can be stated within the lan- guage of ZFC. From this important position, the axioms of ZFC can be seen as the axioms of all of mathematics and hence the axioms of exact reasoning itself.3 Fraenkel was born in Munich in 1891 to a fairly well known Orthodox Jewish German family whose lineage includes people such as his great-grandfather B. H. Auerbach, the publisher of the (now infamous) Sefer ha-Eshkol.4 Like many German students, he studied in various universities, including the universities of Berlin, Munich, Marburg, and Breslau before receiving his PhD in mathe- matics. He served as a German soldier, mostly in a medical capacity, for 50 months in WWI. During that period he met many kinds of Jews and developed the Jewish world-view that would stick with him for the rest of his life. Shortly after returning from war, he met Wilhelmina Malka A. Prins who was studying German at the time. They married in 1920. He thought their partnership was ideal be- 2 The paradoxes that show that Cantor’s original set theory is inconsistent. Russell’s paradox from 1902 (first discovered by Zermelo) is similar to the “Barber Paradox.” If there is a lone barber in an isolated town who shaves all and only those people who do not shave themselves, who shaves the barber? If he shaves himself, then he doesn’t shave himself, and if he doesn’t, then he does. In set theory, you can have a “barber set” that is made up of those kinds of elements that cause analogous problems. The Burali-Forti paradox (1897) is more complicated and involves the largest ordinal number in the set of ordinal numbers. 3 The discussion of ZFC is loosely adapted from Noson Yanofsky’s forth- coming The Outer Limits of Reason. 4 (Fraenkel 1967, 13) fails to mention the controversy over this work. It is possible Fraenkel was not aware that it might have been a forgery. See Mark B. Shapiro’s note for more on the provenance of Sefer ha-Eshkol: <http://seforim.traditiononline.org/index.cfm/Besamim%20Rosh>. A. A. Fraenkel’s Philosophy of Religion : 211 cause apart from religion and Zionism, they had no interests in common. They complemented each other perfectly and would eventually have four children together. After the war, Fraenkel taught mathematics in the university of Marburg from 1922 and then in Kiel from 1928. Though he claims to have experienced no anti-Semitism at either Marburg or Kiel prior to 1933 (Fraenkel 1967, 185) he decided to try teaching in the newly opened Hebrew University in Jerusalem. He stayed there for two years from 1929 to 1931, but was compelled to return to Kiel because of the poor economic situation in Palestine. When the Nazis came to power a year later he was forced to leave Kiel. The American Friends of He- brew University sponsored his professorship and he was able to re- turn to Hebrew University where he remained until his retirement in 1959.5 In mandate Palestine and then in Israel, he was a member of various national boards and councils of the Yishuv (Jewish Set- tlement in Palestine) and was an indefatigable educator throughout. Fraenkel was initially hesitant to join the newly opened He- brew University as it was Jewish but avowedly secular. He recounts in his autobiography that he wrote to Rabbi Abraham Isaac Kook— a man for whom he expresses great respect (see Fraenkel 1967, 191)—asking if it was appropriate, given its secular Jewish orienta- tion, to join the faculty of the Hebrew University. Fraenkel was worried that the Hebrew University would be a forum for heretical “scientific” studies of the Bible and Jewish sacred texts.6 Rav Kook 5 Two useful books about Jewish mathematicians and mathematics under the Nazis are (Segal 2003) and (Siegmund-Schultze 2009). The latter book also contains references to archives that contain material and biographical information about Fraenkel, as does (Katz 2004) and (Katz 1997). 6 (Fraenkel 1918) first addresses this question. (The article was published with a response by Harry Torczyner, who coincidentally would later go on to win the Israel Prize in the same year as Fraenkel.) A few years later he raises related questions in (Fraenkel 1924). That article generated a number of replies in the following issue of the journal, some (e.g., that of Ch. Tschernowitz) quite sharp, to which he responded a few months later in (Fraenkel 1924b). (Fraenkel 1924) also reproduced a letter from Rabbi D. Hoffmann, the head of the Berlin Rabbinical Seminary, to Fraenkel, in support of a Jewish university urging the Orthodox to participate in such a university so as not to be absent from any debate (cf. Rav Kook’s 212 : Hakirah,̣ the Flatbush Journal of Jewish Law and Thought characteristically replied that it was indeed Fraenkel’s responsibility to participate in the university and thereby elevate its spiritual level. Asking R. Kook about joining the faculty of a Jewish and secular Hebrew University was no case of false piety. Fraenkel was deeply bothered by the nature of the university years before it opened its doors and wrote a number of articles grappling with this dilemma. In 1924, prior to the opening of the university, he argued that it would be offensive to the believing Jew to establish an institution in the heart of the Jewish homeland that took stances on religious top- ics like Bible study that were staunchly antithetical to the religious viewpoint: “…teachings dissenting from Judaism have cheerfully been given hospitality in this or that Seminary or Yeshibah (sic), but the adoption of a definite viewpoint in the locality which aims to embody the highest scientific instance of universal Judaism, will rightfully be considered by the Jew everywhere throughout the world who is convinced of the opposite, and doubly so by the Pal- estinian Jew, as the gravest insult to his holiest feelings, and will be correspondingly combated. To conjure up such a cultural struggle means to assume a terrible responsibility” (Fraenkel 1924: 30, em- phasis in original). In addition to R. Kook, Fraenkel’s autobiography recounts con- tact with many interesting Jewish, Zionist, and scientific figures.7 Not only was he acquainted with many of the more interesting per- sonalities, he was also engaged with them on a religious level. He was called upon to weigh in on one of the more famous Jewish legal questions of the day: what day to fast on Yom Kippur in Japan? This question was hotly debated when in 1941 Jewish refugees who found themselves in Japan during World War II sent an urgent tele- gram to Rabbi Herzog, the Chief Rabbi of Palestine, to verify the correct day to fast for Yom Kippur. The question hinges on wheth- reply below). Hoffman also felt it was important to avoid a “culture war” between the religious and secular. 7 For example, he corresponded with Niels and Harald Bohr, Husserl, Koyré, von Neumann, and especially Einstein, who eventually convinced Fraenkel to consider alternate views in the philosophy of mathematics. Fraenkel also mentions the many talks he had with Einstein about reli- gion (Fraenkel 1967, 172). A. A. Fraenkel’s Philosophy of Religion : 213 er the International Date Line tracks the change from one day to the next in the same place as Jewish law.